On the convergence rate of the fraction of simple algebras. (English) Zbl 1459.08001

If \(P(S,A{\lg _{\rho ,n}})\) is the fraction of simple \(n\)-element algebras of finite type \(\rho \) containing at least one operation symbol of arity \(k \geqslant 3\), then \(P(S,A{\lg _{\rho ,n}}) \geqslant 1 - \exp ( - {n^{k - 1}} + 2{n^{k - 2}} + n\ln (n))\).


08A30 Subalgebras, congruence relations
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